With a $500 budget you may have to make some compromises. You're running two monitors which means you need a bit more horsepower than a single screen. Arma 3 is a pretty cpu intensive game, the amd apu's are a bit weaker than the fx chips and those fall behind intel's chips. You should be able to hit 60fps in arma 3 on very high settings with a single gtx 970 at around 1080 but paired with a stronger cpu as well.
Depending on how you do it, most people go with 3 screens with the hud in the center screen or if you have the game on one screen and menu's on the other. With it set like that, menu's on one and gameplay on just one screen the fps would be better than stretching across 2 screens.
Dayz has been having issues, or at least it was a couple months ago. I don't play it personally so can't speak from experience though many agree it's another cpu intensive game. Low fps can be improved with something like an i5, but that means new cpu, motherboard, windows reinstall (if you had oem that came with a prebuilt you'll likely have to purchase a new license) and it cuts into your budget for a better gpu pretty heavily. Lag can be game dependent on a game that's either poorly optimized as dayz has been, if playing multiplayer it could be your internet connection or the game server. If its the server, you can dump $1000 into a new i7 build and it won't help much.
Just trying to look at all angles, upgrades will help but rather than spend $500 or more and expect 60+ fps on dual monitors and lag free play on all these games to find out otherwise or to feel you wasted your money. For a cpu + gpu upgrade for these games you may be looking at closer to $600. Even looking to an fx 8320/8350 over a locked core i5 won't change the overall price much. If you had to purchase a new copy of windows (8.1) you're looking at around $620-660 regardless if you go with amd or intel + the gtx 970 + os.
A 960 is cheaper and better than what you currently have but at 1080p on a single monitor in arma3 on ultra you're looking at more like 40-48fps. With your current cpu I'd expect it to be lower. You might get closer to 60fps in arma3 with an i5 and 960 if you turn some of the detail down to med/high. Again that's single screen though.
http://www.tomshardware.com/reviews/nvidia-geforce-gtx-960,4038-4.html
PCPartPicker part list /
Price breakdown by merchant
CPU: Intel Core i5-4590 3.3GHz Quad-Core Processor ($186.99 @ NCIX US)
Motherboard: ASRock H97 Anniversary ATX LGA1150 Motherboard ($71.89 @ OutletPC)
Video Card: EVGA GeForce GTX 970 4GB Superclocked ACX 2.0 Video Card ($314.99 @ NCIX US)
Operating System: Microsoft Windows 8.1 OEM (64-bit) ($86.98 @ OutletPC)
Total: $660.85
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-08-30 06:00 EDT-0400
PCPartPicker part list /
Price breakdown by merchant
CPU: AMD FX-8320 3.5GHz 8-Core Processor ($136.99 @ NCIX US)
CPU Cooler: Cooler Master Hyper 212 EVO 82.9 CFM Sleeve Bearing CPU Cooler ($24.89 @ OutletPC)
Motherboard: Asus M5A99X EVO R2.0 ATX AM3+ Motherboard ($97.99 @ Newegg)
Video Card: EVGA GeForce GTX 970 4GB Superclocked ACX 2.0 Video Card ($314.99 @ NCIX US)
Operating System: Microsoft Windows 8.1 OEM (64-bit) ($86.98 @ OutletPC)
Total: $661.84
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-08-30 06:07 EDT-0400
Just a note, the reason for the cooler an better quality motherboard with the amd build, you're going to want to overclock it if going that route. The amd cpu's struggle on single core performance which greatly affects both those games you mentioned. The 4590 doesn't overclock (doesn't need to, has higher ipc performance) so can get by on the stock cooler. The inclusion of windows is worst case scenario if you're stuck with an oem copy of windows that came with the pc. If you have a copy of windows and don't need it, that can be skipped.
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